Reaction-diffusion systems with initial data of low regularity
| Autor: | Benoît Perthame, El-Haj Laamri |
|---|---|
| Přispěvatelé: | Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Modelling and Analysis for Medical and Biological Applications (MAMBA), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Benoît Perthame has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 740623), European Project: 740623,H2020 Pilier ERC,ADORA(2017), Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité) |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Property (philosophy)
Quadratic systems 01 natural sciences Lotka-Volterra L 2 estimate Mathematics - Analysis of PDEs Semi-linear parabolic equations Reaction–diffusion system FOS: Mathematics Applied mathematics [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] Reaction-diffusion system 0101 mathematics Control (linguistics) Global existence Mathematics Applied Mathematics Nonlinear diffusion 010102 general mathematics Parabolic partial differential equation 010101 applied mathematics Chemical kinetics 2010 Mathematics Subject Classification. 35K10 35K40 35K57 Super-linear growth Key (cryptography) A priori and a posteriori 2010 Mathematics Subject Classification : 35K10 35K40 35K57 Analysis Analysis of PDEs (math.AP) |
| Zdroj: | Journal of Differential Equations Journal of Differential Equations, Elsevier, 2020, 269 (11), ⟨10.1016/j.jde.2020.06.042⟩ Journal of Differential Equations, 2020, 269 (11), ⟨10.1016/j.jde.2020.06.042⟩ |
| ISSN: | 0022-0396 1090-2732 |
| DOI: | 10.1016/j.jde.2020.06.042⟩ |
| Popis: | Models issued from ecology, chemical reactions and several other application fields lead to semi-linear parabolic equations with super-linear growth. Even if, in general, blow-up can occur, these models share the property that mass control is essential. In many circumstances, it is known that this L 1 control is enough to prove the global existence of weak solutions. The theory is based on basic estimates initiated by M. Pierre and collaborators, who have introduced methods to prove L 2 a priori estimates for the solution. Here, we establish such a key estimate with initial data in L 1 while the usual theory uses L 2 . This allows us to greatly simplify the proof of some results. We also establish new existence results of semilinearity which are super-quadratic as they occur in complex chemical reactions. Our method can be extended to semi-linear porous medium equations. |
| Databáze: | OpenAIRE |
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